The sum of $6$ consecutive integers is $471$. What is the fifth number in this sequence?
Answer: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $6$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 471$ $6x + 15= 471$ $6x = 456$ $x = 76$ Since $x$ is the first number, $x + 4$ is the fifth integer. Thus, the fifth number in the sequence is $80$.